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Have an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.

Suppose a sector of a circle with radius r has a central angle of  θ

. Since a sector is a fraction of a __________ circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle to the measure of a full rotation of the circle. A full rotation of a circle is  2π  radians. This proportion can be written as  A/πr2=_____________ Multiply both sides by  πr2  and simplify to get ________, where  θ  is the measure of the central angle of the sector and r is the radius of the circle.

 

Please help guys, you rock! I am not very good at proofs haha

wertyusop  Jan 19, 2018
edited by wertyusop  Jan 19, 2018
 #1
avatar+89715 
+2

The stuff in red goes into each respective blank

 

 Whole

 

 Note, werty.....that the second blank can be interpreted like this :

 

A /  [ pi r^2 ]   =   θ / [ 2pi ]           [ multiply both sides by pi r^2  ]

 

A  =  [ θ / 2 ]  r^2  =    (1/2)r^2 θ

 

 

cool cool cool

CPhill  Jan 19, 2018
edited by CPhill  Jan 20, 2018
 #2
avatar+38 
+1

Awesome, that does look right. Thanks for explaing and making it easier CPhill. laugh

wertyusop  Jan 19, 2018

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